WASHINGTON (CNN) -- Leading Senate Republicans indicated Sunday that a filibuster on Sonia Sotomayor's nomination to the U.S. Supreme Court is unlikely, though they also promised not to shy away from what they characterized as a troubling judicial record.

Federal Judge Sonia Sotomayor has made decisions that worry some Republican leaders.

Reflecting the delicate political balancing act of opposing the nation's first Hispanic nominee for the Supreme Court, they also pushed back against those conservative commentators who were quick to paint Sotomayor as a racist.

"I don't think that the need for filibuster will be there unless we have not had a chance to look at the record fully," Sen. Kay Bailey Hutchison, R-Texas, told CNN's John King on "State of The Union."

"I have voted [against filibustering] sometimes even when I voted against the nominee if I felt that I knew enough about the nominee. I think it will be determined in that way."

Senate Minority Leader Mitch McConnell, R-Kentucky, told King he had "no earthly idea whether [a filibuster] would be appropriate," but noted that he had consistently voted against filibustering judicial nominees during the last Democratic administration.

Alabama Sen. Jeff Sessions, the ranking Republican on the Senate Judiciary Committee, struck a similar tone, arguing that "filibusters should not be used readily and ought to be [only] for extraordinary circumstances."

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A filibuster would be "unlikely, but we'll have to see how this hearing plays out," Sessions said on NBC's "Meet the Press."

But Sen. John Cornyn, R-Texas, on ABC's "This Week," responded to a question about a possible filibuster by saying, "It's really premature to say that or to speculate."

Meanwhile, one of the Senate's top Democrats, Sen. Chuck Schumer of New York, told ABC, "I think she's virtually filibuster-proof when people learn her record and her story."

But the GOP leadership did not back away from criticizing Sotomayor in a number of areas.

McConnell took aim at the judge's ruling in the 2008 case Ricci v. DeStefano, where Sotomayor backed the decision by the city of New Haven, Connecticut, to throw out the results of a firefighter promotion exam because almost no minorities qualified for promotions.

"The Department of Justice, under the Obama administration, disagrees with the decision Justice Sotomayor made. Her colleague on that circuit, [Judge] Jose Cabranes, also appointed by President Clinton, vigorously disagreed with the decision. ... So I think it is certainly worth looking at."

The U.S. Supreme Court is set to rule on an appeal of Sotomayor's decision by the end of its current term in June.

McConnell also highlighted Sotomayor's controversial remarks at a 2005 panel discussion at Duke University, where she told students that the federal Court of Appeals is where "policy is made [and] where ... the law is percolating."

"Those of us who are elected are supposed to make policy, but those of us who are appointed are supposed to apply the law," McConnell argued.

Hutchison added she was troubled "to hear someone say something like ... the Court of Appeals is where we make policy in this country."

In addition, the Republicans criticized Sotomayor's 2001 speech at the University of California, Berkeley, where Sotomayor said that she "would hope that a wise Latina woman, with the richness of her experiences, would more often than not reach a better conclusion than a white male who hasn't lived that life."

The comment promises to be a focal point of Sotomayor's confirmation hearings over the summer.

"It does trouble me to say that one type of old person versus another one is going to make a different or better decision," Hutchison said.

Conservatives such as talk radio host Rush Limbaugh have seized on Sotomayor's remark, calling her a "reverse racist."

Former House Speaker Newt Gingrich of Georgia wrote in a Twitter post Wednesday, "White man racist nominee would be forced to withdraw. Latina woman racist should also withdraw."

McConnell, however, argued Sunday that the view of Limbaugh and Gingrich "is certainly not my view. My view is we ought to take a look at this nominee's qualifications. I think [Sotomayor's] life story is absolutely impressive."

The White House and other Democratic defenders of Sotomayor have argued that her remarks have been taken out of context.

Sen. Dianne Feinstein, D-California, told CBS' "Face the Nation" that without the word "better," Sotomayor's remark was "a perfectly fine statement. And I understand what she meant by it."

Feinstein added, "I think you have to look at an individual in their total context. This is, in fact, an amazing woman. She is, in fact, the American dream. ... This is a woman that has a very strong spine, has a very good heart, and has had a life that she has worked herself up by her own bootstraps. And that impresses me."

Sen. Amy Klobuchar, D-Minnesota, told CNN's "State of the Union" that Sotomayor "could have chosen different words, but what she is basically saying is: 'Your experience matters.' "

Klobuchar drew a parallel between Sotomayor's remarks and remarks made by Justice Samuel Alito, a Republican appointee, during his 2006 confirmation hearings.

"When I get a case about discrimination," Alito said at the time, "I have to think about people in my own family who suffered discrimination because of their ethnic background or because of religion or because of gender. And I do take that into account."

Alito's remarks are "very similar to some of the things [Sotomayor] said," Klobuchar argued.

In his weekly radio address Saturday, President Obama warned Republicans not to play politics with Sotomayor's nomination.

"There are ... some in Washington who are attempting to draw old battle lines and playing the usual political games, pulling a few comments out of context to paint a distorted picture of Judge Sotomayor's record," Obama said.

"No nominee should be seated without rigorous evaluation and hearing; I expect nothing less. But what I hope is that we can avoid the political posturing and ideological brinksmanship that has bogged down this process, and Congress, in the past."

Obama called on the Senate to begin Sotomayor's confirmation process "without delay."

Sotomayor, a Princeton and Yale graduate, has more than 16 years of federal opinions from which to gauge her proficiency as an arbiter. She spent six years as a district judge and a decade on the 2nd U.S. Circuit Court of Appeals.